Question

Мне нужно ответить на эта задание. В коллекции 10 монет из которых 4 имеют дефекты коллекционер выбирает наугад 7 монет . найти вероятность что 2 из них будут с дефектами. Мне plise, по больше объяснений. пока.

Answer 1

Всего 10 монет:6 без дефекта и 4 с дефектом
Число выбранных наугад 7 монет равно числу сочетаний из 10 по7 и равно
10!/(7!*3!)=7!*8*9*10/(7!*1*2*3)=120  (m)
Число выбранных 2 с дефектом и 5 без дефекта равно произведению сочетаний из 4 по 2 и из 6 по 5 и равно
4!*6!/(2!*2!*5!*1)=2!*3*4*5!*6/(2!*5!*1*2)=36  (n)
Вероятность того,что 2 из выбранных наугад 7 монет равна
 P(n,m)=n/m)= 36/120=0,3

Answer 2

Problem Analysis

To find the probability that 2 out of 7 randomly chosen coins from a collection of 10 coins (4 of which have defects) will have defects, we can use the concept of combinations.

Solution

To calculate the probability, we need to determine the number of favorable outcomes (choosing 2 defective coins out of 4) and the total number of possible outcomes (choosing 7 coins out of 10).

The number of ways to choose 2 defective coins out of 4 is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of items and k is the number of items to be chosen.

In this case, n = 4 (number of defective coins) and k = 2 (number of defective coins to be chosen).

C(4, 2) = 4! / (2!(4-2)!) = 6

The number of ways to choose 7 coins out of 10 is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of items and k is the number of items to be chosen.

In this case, n = 10 (total number of coins) and k = 7 (number of coins to be chosen).

C(10, 7) = 10! / (7!(10-7)!) = 120

Therefore, the probability of choosing 2 defective coins out of 7 is:

P = (number of favorable outcomes) / (total number of possible outcomes) = C(4, 2) / C(10, 7) = 6 / 120 = 0.05

So, the probability that 2 out of the 7 randomly chosen coins will have defects is 0.05 or 5%.

Answer

The probability that 2 out of the 7 randomly chosen coins will have defects is 0.05 or 5%.

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